On Properties of Update Sequences Based on Causal Rejection

We consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under answer set semantics. New information is incorporated into the current knowledge base subject to a causal rejection principle enforcing that, in case of conflicts, more recent rules are preferred and older rules are overridden. Such a rejection principle is also exploited in other approaches to update logic programs, e.g., in dynamic logic programming by Alferes et al. We give a thorough analysis of properties of our approach, to get a better understanding of the causal rejection principle. We review postulates for update and revision operators from the area of theory change and nonmonotonic reasoning, and some new properties are considered as well. We then consider refinements of our semantics which incorporate a notion of minimality of change. As well, we investigate the relationship to other approaches, showing that our approach is semantically equivalent to inheritance programs by Buccafurri et al. and that it coincides with certain classes of dynamic logic programs, for which we provide characterizations in terms of graph conditions. Therefore, most of our results about properties of causal rejection principle apply to these approaches as well. Finally, we deal with computational complexity of our approach, and outline how the update semantics and its refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and Practice of Logic Programming

Designing Software Architectures As a Composition of Specializations of Knowledge Domains

This paper summarizes our experimental research and software development activities in designing robust, adaptable and reusable software architectures. Several years ago, based on our previous experiences in object-oriented software development, we made the following assumption: ‘A software architecture should be a composition of specializations of knowledge domains’. To verify this assumption we carried out three pilot projects. In addition to the application of some popular domain analysis techniques such as use cases, we identified the invariant compositional structures of the software architectures and the related knowledge domains. Knowledge domains define the boundaries of the adaptability and reusability capabilities of software systems. Next, knowledge domains were mapped to object-oriented concepts. We experienced that some aspects of knowledge could not be directly modeled in terms of object-oriented concepts. In this paper we describe our approach, the pilot projects, the experienced problems and the adopted solutions for realizing the software architectures. We conclude the paper with the lessons that we learned from this experience

Propositional semantics for default logic

We present new semantics for propositional default logic based on the notion of meta-interpretations - truth functions that assign truth values to clauses rather than letters. This leads to a propositional characterization of default theories: for each such finite theory, we show a classical propositional theory such that there is a one-to-one correspondence between models for the latter and extensions of the former. This means that computing an extension and answering questions about coherence, set-membership, and set-entailment are reducible to propositional satisfiability. The general transformation is exponential but tractable for a subset which we call 2-DT which is a superset of network default theories and disjunction-free default theories. This leads to the observation that coherence and membership for the class 2-DT is NP-complete and entailment is co-NP-complete.Since propositional satisfiability can be regarded as a constraint satisfaction problem (CSP), this work also paves the way for applying CSP techniques to default reasoning. In particular, we use the taxonomy of tractable CSP to identify new tractable subsets for Reiter's default logic. Our procedures allow also for computing stable models of extended logic programs

Psychological evidence for assumptions of path-based inheritance reasoning

The psychological validity of inheritance reasoners is clarified. Elio and Pelletier (1993) presented the first pilot experiment exploring some of these issues. We investigate other foundational assumptions of inheritance reasoning with defaults: transitivity, blocking of transitivity by negative defaults, pre-emption in terms of structurally defined specificity and structurally defined redundancy of information. Responses were in accord with the assumption of at least limited transitivity, however, reasoning with negative information and structurally defined specificity conditions did not support the predictions of the literature. 'Preemptive' links were found to provide additional information leading to indeterminacy, rather than providing completely overriding information as the literature predicts. On the other hand, results support the structural identification of certain links as redundant. Other findings suggest that inheritance proof-theory might be excessively guided by its syntax

A flexible framework for defeasible logics

Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several logics and, when necessary, combine the representations. In general, such an approach results in a very difficult problem of combination. However, if we can choose the logics from a uniform framework then the problem of combining them is greatly simplified. In this paper, we develop such a framework for defeasible logics. It supports all defeasible logics that satisfy a strong negation principle. We use logic meta-programs as the basis for the framework.Comment: Proceedings of 8th International Workshop on Non-Monotonic Reasoning, April 9-11, 2000, Breckenridge, Colorad

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica

Intuitions and the modelling of defeasible reasoning: some case studies

The purpose of this paper is to address some criticisms recently raised by John Horty in two articles against the validity of two commonly accepted defeasible reasoning patterns, viz. reinstatement and floating conclusions. I shall argue that Horty's counterexamples, although they significantly raise our understanding of these reasoning patterns, do not show their invalidity. Some of them reflect patterns which, if made explicit in the formalisation, avoid the unwanted inference without having to give up the criticised inference principles. Other examples seem to involve hidden assumptions about the specific problem which, if made explicit, are nothing but extra information that defeat the defeasible inference. These considerations will be put in a wider perspective by reflecting on the nature of defeasible reasoning principles as principles of justified acceptance rather than `real' logical inference.Comment: Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR'2002), Toulouse, France, April 19-21, 200